The conflicts have been on vivid display at hearings in states like Pennsylvania, where Highmark, one of the state’s largest insurers, has proposed rate increases averaging 41 percent.

“The health of the citizens of Pennsylvania is worth more than the profits desired by health insurance companies,” Rose Lynd, 35, of Pittsburgh, testified at a hearing in Harrisburg held late last month by the Pennsylvania insurance commissioner, Teresa D. Miller, a former Obama administration official.

Ms. Lynd, a cancer survivor, said her costs were onerous.

“My premiums are more than $600 a month, which is more than our mortgage payment,” Ms. Lynd said. “I am grateful that the Affordable Care Act is here for my family, but I am disappointed by its limitations. All I want is a plan that makes our health care affordable, but it doesn’t exist.”

Highmark defended its request by saying it was paying out more in claims than it was receiving in premiums. Jeff Scheib, the vice president in charge of actuarial services at Highmark, offered a statistic to illustrate the problem.

“There were close to 250 individual A.C.A. policyholders in Pennsylvania who incurred over $100,000 each in claims and then canceled coverage before the end of the year,” Mr. Scheib testified. “This behavior drives up the cost to insure the entire pool, because people use insurance benefits and then discontinue paying for coverage once their individual health care needs have been temporarily met.”

While state insurance commissioners, who review rates, are trying to balance the needs of consumers and insurers in a turbulent market, insurers have extra leverage this year. At least a dozen nonprofit health insurance cooperatives have collapsed, and several big commercial insurers have decided to cut their losses by limiting their participation in the insurance exchanges, the new marketplaces created under the health law.

The problems threaten to shadow Democrats through Election Day. While Hillary Clinton has vowed to “defend and expand” the Affordable Care Act, her Republican opponent in the presidential race, Donald J. Trump, has seized on the issue. At a rally in Fairfield, Conn., on Saturday, he repeated his vow to repeal the health law, saying consumers were facing rate increases greater than they had ever seen.

Ms. Miller, the Pennsylvania commissioner, said that protecting consumers was a top priority. But she said, “The large requests before me this year are not unique to Pennsylvania, unfortunately.” Arthur M. Lucker, a consultant to the Pennsylvania Insurance Department, said insurers had requested rate increases of more than 25 percent in at least 20 states, including Arizona, Florida, Ohio and Texas.

Aviva Aron-Dine, an economist at the federal Department of Health and Human Services, said predictable factors were behind the upward pressure on rates. For example, the federal government is ending a program that helped pay some of the largest claims incurred by insurers.

In addition, Ms. Aron-Dine said, some insurers may be trying to make up for having initially set premiums too low. In any event, she said, most people buying insurance on the exchanges receive subsidies.

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A health insurance fair last year in San Francisco.CreditJim Wilson/The New York Times

Connecticut has a state-run insurance exchange considered one of the most successful in the nation. But that has not provided a guarantee of stable rates.

Anthem, for example, is seeking an average increase of 27 percent in Connecticut.

That is “just off the charts and unacceptable,” one Anthem customer, Douglas H. Wade Jr. of Bridgeport, said at a hearing in Hartford on Aug. 3.

Matthew McDermott, the leader of an interfaith advocacy group, Congregations Organized for a New Connecticut, said: “We’re concerned that the proposed rate increases will drive many employers and many individuals to drop coverage altogether. And we worry that that heads us toward a market failure here in Connecticut.”

Two of the four insurers on the Connecticut exchange have indicated that they will not be offering plans in that marketplace next year. “Higher-than-expected health care costs have jeopardized the financial solvency of some insurers and have caused other insurers to leave the exchange altogether,” said James Augur, a regional vice president of Anthem in Connecticut.

At a hearing in Helena, Mont., Monica J. Lindeen, the state insurance commissioner, asked Blue Cross and Blue Shield why it was seeking an average rate increase of 62 percent for 2017, after receiving an increase of 22 percent this year.

“Cost is what’s really driving our rate increases,” said Michael E. Frank, the president of Blue Cross and Blue Shield of Montana.

“For every dollar we brought in last year, we paid out $1.26 for medical care,” Mr. Frank said. “In the first six months of this year, we have already paid $4.17 million in medical costs for the top 10 individuals. That’s $70,000 a month for those individuals.”

Insurers invariably cite drug costs as a factor driving up premiums. James Spencer, the chief actuary of Blue Cross and Blue Shield of Montana, said 1 percent of prescriptions accounted for 30 percent of pharmacy costs.

Ms. Lindeen wanted to know why Montana Blue Cross and its parent company, Health Care Service Corporation, had not constrained the pay of top executives. The parent company reported total compensation of more than $11 million for its chief executive in 2014. A Blue Cross executive told Ms. Lindeen that executive pay reflected “the size and complexity of our business” and was a tiny share of total expenses.

While the Obama administration has said the federal insurance marketplace is gaining healthier, lower-cost consumers, several insurers said at the hearings that they had not seen a significant improvement.

“Studies concluded that the market would stabilize after absorbing the pent-up demand from the previously uninsured population,” testified Eric Galvin, the chief financial officer of ConnectiCare Insurance Company. But, he said, “rather than stabilize, that cost has continued to skyrocket, and we see no end to that higher level of spending.”

Christopher F. Koller, a former health insurance commissioner in Rhode Island, said he was always concerned that insurers were seeking higher rates than necessary, with the expectation that their requests would be cut back by state regulators.

But even if officials trim proposed rates, consumers can still face substantial increases.

This month New York officials approved rate increases averaging 16.6 percent for individual health insurance plans in 2017, more than twice the average in the state for 2016.

The insurance commissioner in Mississippi approved an average rate increase of 43 percent for Humana, fearing that the company might otherwise leave the state’s insurance exchange, as UnitedHealth intends to do.

And the Kentucky insurance commissioner has approved increases averaging 5.6 percent for Aetna, 22.9 percent for Anthem and 31 percent for Humana.

A version of this article appears in print on , on Page A13 of the New York edition with the headline: Health Insurers Use Reviews, Intended to Constrain Rate Jumps, to Justify Them. Order Reprints | Today’s Paper | Subscribe